ISESCO JOURNALof Science and Technology

ISESCO JOURNAL of Science and Technology Vo l u m e 1 0 - N u m b e r 1 7 - M a y 2 0 1 4 ( 7 7 - 9 1 )

Abstract

Design Procedure of Centrifugal Compressors

The design procedure was carried out for three his paper investicases: without prewhirl gates the developand with high positive 1 ment of a preliminary King Abdulaziz University, prewhirl of 15° and 30°. design method for centriJeddah, Kingdom of Saudi Arabia Design considerations fugal compressors. The 2 Faculty of Engineering El-Mattaria, of mechanical stress for design process starts with Helwan University, Cairo, Egypt the impeller and minithe aerodynamic analysis mum inlet relative Mach E-mail: [email protected] of the preliminary design number are taken into and its reliance on emconsideration. Diffusion pirical rules limiting the factor limitations have also been considered. Selected main design parameters. The procedure is applied to design parameters according to economical considecompressors for pressure ratios of 1.5, 3 and 5 as an rations have been presented for each pressure ratio. example for developing an initial non-dimensional

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Adnan Hamza Zahed1 and Nazih Noaman Bayomi1,2

skeleton design. The skeleton diagrams are presented for different exit blade angles ranging from 0° to -60°.

Keywords: Blade angle, Centrifugal compressor, Diffusion factor, Inlet Mach number.

1. Introduction

the absence of the ability to increase blade tip speeds, this will in turn create the need to further reduce the blade backsweep in order to achieve the desired pressure ratio. Consequently the application of an inlet prewhirl can be considered in order to reduce the inlet relative Mach number and increase the compressor operating range.

The design of a centrifugal compressor is constrained by a number of non-aerodynamic considerations. These include cost, overall frame size, inertia of the rotating components and general durability. Obtaining high pressure ratios through increased impeller tip speeds dictates the use of titanium metal instead of aluminum, which generates an increase in cost. Current requirements are however for pressure ratios that can be achieved at rotational speeds suitable for aluminum impellers, and the need to switch to alternative material is not yet overwhelming. If the impeller tip speed is considered to be limited by stress considerations, the increase in pressure ratio can only be achieved by reducing the magnitude of the impeller blade backsweep. This will lead to a reduction in operating range which could possibly be recovered through the application of a positive swirl at the impeller inlet. In

The effect of extended front and backward-swept shrouded impellers on the performance of centrifugal compressors with vaneless diffusers was investigated by Sapiro [1]. Japikse and Osborne [2 & 3] introduced an overall performance and a test procedure for the optimization of industrial centrifugal compressors. The results of detailed interstage measurements were presented and the diffusion levels with the compressor components were quantified. A review of some of the theoretical and experimental techniques used in the aerodynamic development of standard stages for

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A.H. Zahed and N.N. Bayomi / ISESCO Journal of Science and Technology - Volume 10, Number 17 (May 2014) (77-91)

industrial centrifugal compressors was presented by Dalbert et al. [4]. Design methods for standardized families of radial compressor stages were summarized. A simple method for designing the blade geometry of a centrifugal compressor impeller was presented by Wang et al. [5]. In this method, instead of giving the mean swirl distribution on the meridional surface, the blade angle distribution was specified and the blade shape was derived, making it easier to execute the design.

centrifugal compressor to lower flowrates compared with a zero prewhirl. Kassens and Rautenberg [15] tested a centrifugal compressor with adjustable IGV with different adjustment angles at -30°, 0°, 30° and 60°. Abdel Hafiz and Bayomi [16] described a procedure for the design of centrifugal compressor impellers. The design procedure has been applied to compressors with moderate pressure ratios. In this work, the effect of the inlet prewhirl on the compressor maps is taken into consideration only for a pressure ratio of 6 for a certain exit blade angle -30°.

In spite of the variations in size, duty and design emphasis, much of the science and understanding that support the aerodynamic and mechanical design of centrifugal compressors are common to all types. Thus, Came and Robinson [6] introduced the aerodynamic design of the centrifugal compressor by computational fluid dynamics (CFD), while Pourfarzaneh et al., [7] introduced a new analytical model of a centrifugal compressor.

The present paper describes the design of centrifugal compressors with three different pressure ratios of 1.5, 3 and 5. The preliminary design of impeller dimensions and impeller aerodynamics are presented. The design procedure depends on a nondimensional method and introduces a simple skeleton for the preliminary design of the impeller. The impeller blade angle varied from radially blade to high lean backward with an angle of -40° and -60°. In addition, an inlet prewhirl is introduced varying from 0° to 30° according to aerodynamic design and stress considerations. The diffusion ratio through the impeller is taken into consideration.

Dalbert et al. [8] described the special design features of a radial compressor and shed light on a method of standardization to overcome the large diversity of machine types. Their paper reviews the aerodynamic and thermodynamic aspects in the design of an impeller with an exit blade angle of up to 75°. Also, Schiffmann & Favrat [9] manage the optimizing of the compressor design into the possible specifications field while keeping high efficiency on a wide operating range.

2. Consideration of the preliminary design 2.1 Importance of the preliminary design The aim of the preliminary design can be simply stated as the desire to achieve the design duty on a onedimensional basis, within the mechanical limitations of available material and with the best achievable efficiency and surge margin. This can be expanded into the following more specific aims: at the design mass flow, or nominal point mass flow, to achieve the desired work input, the desired efficiency, the desired pressure ratio and sufficient surge margin.

Whitfield et al. [10] studied the compressor performance using an inlet guide vane (IGV), with angles varying from -20° to 20° and cambered blades with discharge angle changes from β2= -5° to 35°. The results showed clearly that the improvement in flow range and the isentropic efficiency penalties are considered. In Simon et al. [11] found that the operating range of centrifugal flow compressors with backward curved impeller blades, β2= 50° and 65°, could be extended with IGV and diffuser vanes. Also, Rodgers [12] and Coppinger & Swain [13] concluded that the stable operating range of centrifugal compressors extended by the regulation of the IGV and increased impeller stability. In [14], Whitfield et al. showed that the application of a 55° prewhirl causes a distinct shift in the surge point of the

2.1.1 Work input The main components of a centrifugal compressor are shown in Figure 1. Velocity triangles at inlet and exit of the compressor for radial blades and leaned blades with states of the prewhirl are also plotted in Figure 1.

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The work input to the compressor is usually expressed as the work input factor or stage loading:

Mach number M2, known as C2/a2 can be developed to the following expression:

(1)

(5)

In this equation, the second term of the RHS (right hand side) is known as the slip velocity ratio. It is expressed by Wiesner [17] as (2) Where Z is the number of blades. The third term includes the ratio of the flow velocity in the radial direction, Cr2 and the impeller speed, U2, known as the flow coefficient j and the exit blade angle b∞2. The relation between the work factor and the blade exit angle for different flow coefficients for an impeller of 16 blades is shown in Figure 2. From this figure, it can be deduced that the work factor is reduced at higher values of exit blade angle depending on the velocity ratio Cr2/U2. The work factor is reduced as the flow ratio increases. The work factor also determines the impeller tip speed and consequently the impeller stress levels. The stage pressure ratio obtained from a given tip speed is represented by the equation:

Figure 1. Main component of a centrifugal compressor with velocity triangles at inlet and exit.

(3)

Figure 2. Effect of the exit blade angle on the work factor for different flow coefficients.

2.1.2 Compressor efficiency

The parameter λ = ΔH/(U2)2 = Cu2/U2 = m/[1-(tan β2/tan α2) is often refereed to as the work input coefficient or work factor (Rodgers [12]). Also, the rotational speed is expressed by the “tip speed Mach number” or “stage Mach number”, relating the tip speed U2 to the inlet speed of sound:

Generally, a centrifugal compressor is required to produce a specified pressure ratio at maximum efficiency. The desire to achieve maximum efficiency may be compromised in order to meet other design restraints such as minimizing overall size and weight and maximizing the flowrate between surge and choke. There is a specific non-dimensional flowrate θ at a certain non-dimensional speed Mu2 where maximum efficiency will be achieved. The non-dimensional mass flowrate, θ, can be expressed as

(4) For any specified pressure ratio, the impeller nondimensional tip speed Mu2 follows directly from the equation (3). Alternatively, Mu2 can be systematically varied to cover a range of pressure ratios. The discharge

(6)

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The designer must establish these parameters and then develop the overall geometry of the impeller. The design procedure will be developed beginning from the desired pressure ratio, with specified target efficiencies for the impeller and the complete stage. The impeller efficiency is required to effectively transform the desired stage pressure ratio to that required from the impeller only. However, the desire to maximize this efficiency will be maintained. In addition to establishing the optimum non-dimensional mass flowrate and impeller speed, the non-dimensional geometry of the impeller will be developed in terms of the radius ratio, r1s/r2, the discharge height, b2/r2, and the inlet and discharge blade angles.

4. Clearance loss is due essentially to the gap between the tips of the rotating blades and the stationary shroud. Therefore, the clearance gap should be minimized as much as possible. The proportion of the flow passage occupied by the clearance gap will increase as the actual blade height is reduced, hence the necessity to assess the magnitude of the non-dimensional blade height, b2/r2.

In fact, to maximize efficiency, it is necessary to minimize loss. Whilst losses are not explicitly calculated through the application of loss models, it is essential to assess the consequences of any design choice on loss generating processes. For the impeller, the losses commonly considered are aerodynamic and parasitic losses. The aerodynamic losses and the sequence required for minimizing them are as follows:

Parasitic losses include the disc friction over the hub and shroud disc and losses in connection with the leakage over the hub and shroud labyrinth seals. It was found that the loss rates are independent of the Reynolds number and became minimal at a certain flow coefficient.

5. Diffuser system loss: The high discharge Mach number M2 from the impeller must be diffused. It is therefore important to ensure that the discharge Mach number is not higher than necessary.

The essential aim of the design procedure is to establish the optimum velocity triangles at the inlet to and discharge from the impeller. Specifying and systematically varying the absolute and relative flow angles achieves this. The case of swirl-free flow at the inlet is considered here and the absolute flow angle at the impeller inlet is zero. In the case of the absolute flow angle at the impeller discharge, Johnston and Dean [19] showed that an optimum flow angle α2, for design pressure, lies between 63°to 68°. Similarly, Rodgers and Sapiro [20] considered the optimum flow angle to lie between 60° and 70°. Osborne et al. [21] used a magnitude of 70° in the design of an 8:1 pressure ratio compressor, whilst for a 6.5:1 pressure ratio compressor, Came [22] indirectly used a magnitude of 75°. Came and Robinson [6] found a range of 69°